All tasks in this group require determining the proposition as True or False. All numbers with fixed amount of digits (for example, two-digit number, three-digit number and so on) are assumed to be positive integers.
Boolean1°. Given integer A, verify the following proposition: «The number A is positive».
Boolean2°. Given integer A, verify the following proposition: «The number A is odd».
Boolean3°. Given integer A, verify the following proposition: «The number A is even».
Boolean4°. Given two integers A and B, verify the following proposition: «The inequalities A > 2 and B £ 3 both are fulfilled».
Boolean5°. Given two integers A and B, verify the following proposition: «The inequality A ³ 0 is fulfilled or the inequality B < –2 is fulfilled».
Boolean6°. Given three integers A, B, C, verify the following proposition: «The double inequality A < B < C is fulfilled».
Boolean7°. Given three integers A, B, C, verify the following proposition: «The number B is between A and C».
Boolean8°. Given two integers A and B, verify the following proposition: «Each of the numbers A and B is odd».
Boolean9°. Given two integers A and B, verify the following proposition: «At least one of the numbers A and B is odd».
Boolean10°. Given two integers A and B, verify the following proposition: «Exactly one of the numbers A and B is odd».
Boolean11°. Given two integers A and B, verify the following proposition: «The numbers A and B have equal parity».
Boolean12°. Given three integers A, B, C, verify the following proposition: «Each of the numbers A, B, C is positive».
Boolean13°. Given three integers A, B, C, verify the following proposition: «At least one of the numbers A, B, C is positive».
Boolean14°. Given three integers A, B, C, verify the following proposition: «Exactly one of the numbers A, B, C is positive».
Boolean15°. Given three integers A, B, C, verify the following proposition: «Exactly two of the numbers A, B, C are positive».
Boolean16°. Given a positive integer, verify the following proposition: «The integer is a two-digit even number».
Boolean17°. Given a positive integer, verify the following proposition: «The integer is a three-digit odd number».
Boolean18°. Verify the following proposition: «Among three given integers there is at least one pair of equal ones».
Boolean19°. Verify the following proposition: «Among three given integers there is at least one pair of opposite ones».
Boolean20°. Given a three-digit integer, verify the following proposition: «All digits of the number are different».
Boolean21°. Given a three-digit integer, verify the following proposition: «All digits of the number are in ascending order».
Boolean22°. Given a three-digit integer, verify the following proposition: «All digits of the number are in ascending or descending order».
Boolean23°. Given a four-digit integer, verify the following proposition: «The number is read equally both from left to right and from right to left».
Boolean24°. Three real numbers A, B, C are given (A is not equal to 0). By means of a discriminant D = B2 – 4·A·C, verify the following proposition: «The quadratic equation A·x2 + B·x + C = 0 has real roots».
Boolean25°. Given two real numbers x, y, verify the following proposition: «The point with coordinates (x, y) is in the second coordinate quarter».
Boolean26°. Given two real numbers x, y, verify the following proposition: «The point with coordinates (x, y) is in the fourth coordinate quarter».
Boolean27°. Given two real numbers x, y, verify the following proposition: «The point with coordinates (x, y) is in the second or third coordinate quarter».
Boolean28°. Given two real numbers x, y, verify the following proposition: «The point with coordinates (x, y) is in the first or third coordinate quarter».
Boolean29°. Given real numbers x, y, x1, y1, x2, y2, verify the following proposition: «The point (x, y) is inside of the rectangle whose left top vertex is (x1, y1), right bottom vertex is (x2, y2), and sides are parallel to coordinate axes».
Boolean30°. Given three integers a, b, c that are the sides of a triangle, verify the following proposition: «The triangle with sides a, b, c is equilateral».
Boolean31°. Given three integers a, b, c that are the sides of a triangle, verify the following proposition: «The triangle with sides a, b, c is isosceles».
Boolean32°. Given three integers a, b, c that are the sides of a triangle, verify the following proposition: «The triangle with sides a, b, c is a right triangle».
Boolean33°. Given three integers a, b, c, verify the following proposition: «A triangle with the sides a, b, c exists».
Boolean34°. Given coordinates x, y of a chessboard square (as integers in the range 1 to 8), verify the following proposition: «The chessboard square (x, y) is white». Note that the left bottom square (1, 1) is black.
Boolean35°. Given coordinates x1, y1, x2, y2 of two chessboard squares (as integers in the range 1 to 8), verify the following proposition: «Both of the given chessboard squares have the same color».
Boolean36°. Given coordinates x1, y1, x2, y2 of two chessboard squares (as integers in the range 1 to 8), verify the following proposition: «A rook can move from one square to another during one turn».
Boolean37°. Given coordinates x1, y1, x2, y2 of two chessboard squares (as integers in the range 1 to 8), verify the following proposition: «A king can move from one square to another during one turn».
Boolean38°. Given coordinates x1, y1, x2, y2 of two chessboard squares (as integers in the range 1 to 8), verify the following proposition: «A bishop can move from one square to another during one turn».
Boolean39°. Given coordinates x1, y1, x2, y2 of two chessboard squares (as integers in the range 1 to 8), verify the following proposition: «A queen can move from one square to another during one turn».
Boolean40°. Given coordinates x1, y1, x2, y2 of two chessboard squares (as integers in the range 1 to 8), verify the following proposition: «A knight can move from one square to another during one turn».